Vadose Zone Journal

Quantifying Topographic and Vegetation Effects on the Transfer of Energy and Mass to the Critical ZoneCraig Rasmussen,* Jon D. Pelletier, Peter A. Troch, Tyson L. Swetnam, and Jon ChoroverCritical zone evolution, structure, and function are driven by energy and mass fluxes into and through the terrestrial subsurface. We have developed an approach to quantifying the effective energy and mass transfer (EEMT, MJ m−2 yr−1) to the subsurface that accounts for local variations in topogra-phy, water and energy balances, and primary production. Our objectives were to quantify how (i) local topography controls coupled energy and water transfer to the subsurface, and (ii) vegetation effects on local-scale evapotranspiration and primary production controls of energy and mass transfer to the critical zone, both at the pedon- to hillslope-scale resolu-tion, in the context of quantifying controls on EEMT. The model was tested across a semiarid environmental gradient in southern Arizona, spanning desert scrub to mixed conifer ecosystems. Data indicated clear variations in EEMT by topography, via both aspect and local water redistribution, and with current vegetative cover. Key findings include: (i) greater values of EEMT on north-facing slopes in a given elevation zone, with a north-facing aspect equivalent to an ?300-m elevation gain; (ii) a power law relationship between aboveground biomass and EEMT, with disturbance in the form of stand-replacing wildfire substantially reducing estimates of EEMT; and (iii) improved correlation of EEMT to pedon-scale variations in critical zone struc-ture with EEMT values that include topography. Incorporating greater levels of environmental variation and complexity presents an improved approach to estimating the transfer of energy and mass to the subsurface, which is important to our understanding of critical zone structure and function.

Abbreviations: AET, actual evapotranspiration; CZ, critical zone; DEM, digital elevation model; EEMT, effective energy and mass transfer; LAI, leaf area index; MCWI, mass con-servative wetness index; NAIP, National Agriculture Imagery Program; NPP, net primary production; PET, potential evapotranspiration; PPT, precipitation; SCM, Santa Catalina Mountains.

The evolution, structure, and function of the critical zone (CZ), the zone that extends from the top of the canopy down to the groundwater, is driven by energy and mass fluxes into and through the terrestrial subsurface. Internal fluxes and spatial structure coevolve in response to the transfer and transformation of energy and mass through the CZ system. Quantifying these fluxes is central to understanding CZ evolution and func-tion at both short (10−3– 102 yr) and long (103– 106 yr) time scales and to predicting the ability of the CZ to provide key services to society. Flux quantification represents a major challenge to CZ science (National Research Council, 2010), with a particular challenge in quantifying the relative importance of the influxes of water, C, radiation, etc., on driving CZ evolution and function. Placing these CZ influxes into the common currency of energy per unit area per unit time has shown significant promise in addressing this challenge across relatively “simple” landscapes, i.e., ignoring the complexities that local variations in topography and vegetation structure introduce into energy and mass influxes to the CZ. In this study, we further developed an energy metric approach to account for topographic

We have developed an improved method for measuring the transfer of energy and mass, in the form of water and carbon, to the subsur-face critical zone. These transfers are fundamental to earth surface function and evolution.

C. Rasmussen, T.L. Swetnam, and J. Chorover, Dep. of Soil, Water and Envi-ronmental Science, Univ. of Arizona, Tucson, AZ 85719; J.D. Pelletier, Dep. of Geosciences, Univ. of Arizona, Tucson, AZ 85719; P.A. Troch, Dep. of Hydrology and Water Resources, Univ. of Arizona, Tucson, AZ 85719; and T.L. Swetnam, School of Natural Resources and the Environment, Univ. of Arizona, Tuc-son, AZ 85719. *Corresponding author (crasmuss@cals.arizona.edu).

Vadose Zone J. doi:10.2136/vzj2014.07.0102Received 31 July 2014.Accepted 19 Nov. 2014.Supplemental material online.

Original Research

© Soil Science Society of America 5585 Guilford Rd., Madison, WI 53711 USA.All rights reserved.

Published November 13, 2015

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and vegetation controls on CZ energy and mass influxes at pedon- to hillslope-scale (e.g., 10 m pixel−1) resolution.

Recent work quantifying the transfer of energy and mass to the CZ via C derived from net primary production and water in excess of evapotranspiration indicates that these relatively simple-to-derive terms exhibit strong correlations with a range of CZ structural and functional properties (Rasmussen et al., 2011). The transfer term is referred to as “effective energy and mass transfer” (EEMT) because, while the C and water terms approximate only a fraction of the total energy and mass balance of CZ systems, these fluxes are deemed highly relevant to predicting subsurface physical, chemical, and biological properties. The previous applications of EEMT have largely been derived using relatively coarse-resolution temperature and precipitation data and temperature-based estimates of evapo-transpiration that do not account for topographic and vegetative controls on local-scale water partitioning and primary production (Rasmussen, 2012; Rasmussen and Gallo, 2013; Rasmussen et al., 2005; Rasmussen and Tabor, 2007). This technique works well at regional scales and for describing broad patterns of CZ local development when arrayed across a large climate space. However, to accurately model catchment- to hillslope-scale EEMT, local topographic and vegetative factors controlling energy, water, and C transfer (including lateral fluxes) must be incorporated. For exam-ple, it is widely recognized across earth science disciplines that significant differences in water availability and hence CZ structure often occur on north- vs. south-facing hillslopes within the same region and elevation, particularly in water-limited environments (Broxton et al., 2009; Gutierrez-Jurado and Vivoni, 2013; Melton, 1960; Pelletier et al., 2013; Poulos et al., 2012). Previous methods for computing EEMT did not adequately honor such local, microclimatic variations. The empirical model for calculating EEMT presented by Chorover et al. (2011) used vapor pressure deficit and topographically modified temperature as a means to intro-duce topographic controls on local EEMT rates; however, this formulation was purely correlative and did not include theory grounded approximations of topographic effects on pedon- to hillslope-scale water, energy, and C balances.

This study addressed the overarching question of how topography and vegeta-tion affect local-scale estimates of EEMT. Our objective, therefore, was to develop a methodology for calculating how (i) local topography controls coupled energy and water balances and (ii) vegetation affects local-scale evapotranspiration and pri-mary production and how this variation affects estimates of EEMT. Unique sets of

values for EEMT that incorporate varying levels of topographic and vegetation information were then compared with a simple metric of CZ structure—soil depth—to demonstrate the relative improvement in the relationship between EEMT and pedon- to hillslope-scale CZ structural variation imparted by incorporation of greater topographic complexity into the EEMT framework. The EEMT framework applied here is just one specific approach for quantifying energy and mass transfer to the CZ, but the use of solar radiation to modify the local temperature and vapor pressure deficit along with topographic controls on water redistribution are central and relevant to any effort to quantify how topography influences CZ energy and water availability.

6Conceptual FrameworkThe EEMT framework is built around the premise that CZ pro-cesses and evolution are a direct function of gradient-driven fluxes of energy and mass, including solar radiation, C, water, and the mineral or sediment supply. Cycling and storage of energy and mass occurs through processes such as infiltration and recharge, primary production and C cycling, physical and chemical weath-ering, and erosion and sediment transport. Export of energy and mass occurs through evapotranspiration, CO2 respiration, runoff and base flow, and denudation (Fig. 1). The CZ may thus be con-ceptualized to function as an open thermodynamic system wherein the flux of energy and mass into and through the system drives internal cycling processes that result in the formation of organized structures. These structures optimize energy and mass storage as well as system export of dissipative products. Quantifying the rel-evant influx of energy and mass provides a predictive capability

Fig. 1. Conceptual framework characterizing major fluxes and processes in the critical zone. The fluxes may be quantified in terms of energy and mass balance terms, with the total energy trans-ferred to the critical zone (ETotal) the sum of energy associated with evapotranspiration (EET), precipitation (EPPT), net primary production (EBIO), erosion and sediment transport (EELEV), geochemical gradients (EGEO), and any other energy and mass transfers Ei) Effective energy and mass transfer (EEMT) is equal to the net energy and mass fluxes associated with effective precipita-tion (EePPT) and net primary production (EBIO) (modified from Rasmussen, 2012; artwork from Chorover et al., 2007).

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for quantifying CZ processes and structural organization under the hypothesis that greater energy and mass flux results in greater structural organization and output of dissipative products (Rasmussen et al., 2011).

The EEMT framework was developed from the classic soil-forming factor approach (Jenny, 1941) that states that soil properties are a function of climate, biota, relief, parent material, and landscape age. Rasmussen (2012) restated this as: CZ = f(T, VPD, PPT, Rn, C, S)tr, where CZ is the critical zone state, T is the temperature, VPD is the vapor pressure deficit, PPT is precipitation, Rn is net solar radiation, C is the carbon content, S is the mineral supply and sediment transport, and tr is the relative age of the system, which explicitly links each factor with key CZ energy and mass balances. Volobuyev (1964) attempted to formalize these factors into quantitative energy terms and stated that soil properties could be equated to the summation of energy and mass fluxes associ-ated with soil development, where development refers to chemical alteration, structure formation, and the layering, zonation, and organization of the weathered regolith. The summation of these fluxes was stated as (Minasny et al., 2008): E = w1 + w2 + b1 + b2 + e1 + e2 + g + v, where E is the energy involved in soil forma-tion, w1 is the energy of physical rock weathering, w2 is the energy for chemical weathering, b1 is the energy accumulating in the soil organic matter, b2 is the energy for soil organic matter transfor-mation, e1 is the energy for evaporation from the soil surface, e2 is the energy for transpiration, g is the energy losses in leaching of salts and fine materials, and v is the energy expended by the process of heat exchange between the soil and the atmosphere, generally negligible across the centurial to millennial time scales of soil formation.

Rasmussen et al. (2011) took a similar approach and derived this basic statement from the respective energy, water, C, and sediment balances that occur on the Earth’s surface, including tectonically forced gravity-driven sediment transport, and the geochemical alteration of primary and secondary mineral phases (J m−2 s−1), stated as

Total ET PPT BIO ELEV GEO iE E E E E E E= + + + + +å [1]

where EET is the energy and mass flux associated with evapotrans-piration, EPPT is the heat energy associated with precipitation energy and mass transfer, EBIO is the net primary productivity energy and mass transfer, EELEV is the potential energy associated with gravity-driven transport of sediment, EGEO is the geochemi-cal potential of chemical weathering, and Ei is any other external energy and mass input such as dust, anthropogenic inputs, or the heat exchange between the soil and the atmosphere. The EET term by far represents the largest component of ETotal and is typically several orders of magnitude greater than the sum of the remain-ing energy and mass flux terms (Phillips, 2009). However, given that EET represents the transfer of water and radiant energy back

to the atmosphere, it has limited potential for performing chemi-cal or physical work on the subsurface. Equation [1] may thus be restated in terms of energy and mass transferred to the subsurface (ESubsurface, J m−2 s−1):

Subsurface ePPT BIO ELEV GEO iE E E E E E= + + + +å [2]

where the precipitation term, EePPT, denotes effective precipitation, which accounts for precipitation water loss to evapotranspiration. As noted, the EELEV and EGEO terms encompass the physical and chemical transfers of energy and mass associated with denudation and mineral transformation. In many Earth surface systems, the sum of these fluxes may be orders of magnitude less than the water and C flux terms (Phillips, 2009). Therefore, we have focused on the sum of energy and mass transfer associated with effective pre-cipitation and primary production, which Rasmussen et al. (2011) referred to as effective energy and mass transfer (EEMT, J m−2 s−1), defined as:

ePPT BIOEEMT E E= + [3]

where EEMT represents the summation of energy transferred to the subsurface CZ as the heat and mass transfer associated with effective precipitation (EePPT) and chemical energy associated with reduced C compounds derived from primary production (EBIO).

The components of EEMT (Eq. [3]) have units of joules per square meter per second or watts per square meter and may be calculated using relatively simple monthly water balance techniques (e.g., Arkley, 1963) and net primary production estimates (e.g., Lieth, 1975). The value of EePPT (J m−2 s−1) is calculated as

ePPT w E Fc T= D [4]

where F is the mass f lux of water available to move into and through the subsurface (kg m−2 s−1), cw is the specific heat of water (J kg−1 K−1), and DT = Tambient − Tref (K), with Tambient the ambient temperature at the time of water flux and Tref set at 273.15 K. The value of EBIO (J m−2 s−1) is calculated as

BIO BIONPPE h= [5]

where NPP is the mass f lux of C as net primary production (kg m−2 s−1) and hBIO is the specific biomass enthalpy (J kg−1) fixed at a value of 22 ´ 106 J kg−1.

For the purposes of this study, we calculated and compared EEMT derived using three different approaches that incorporated increas-ing levels of complexity and spatial patterns of topography and vegetation. The three methods were: (i) the “traditional” approach based on relatively simple energy and water balances and net primary production estimates (EEMTTRAD); (ii) a modified approach that captures topographic controls on energy, water, and

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C balances (EEMTTOPO); and (iii) an approach that integrates both topographic controls on the water and energy balances and point-scale vegetation controls on surface resistance and primary production (EEMTTOPO-VEG).

6MethodsStudy AreaThe Sabino Creek watershed in the Santa Catalina Mountains (SCM) in southern Arizona, just outside of Tucson, served as the test area for model development and represents well the typical range of climate, vegetation, and soils associated with the Sky Islands of the Desert Southwest (Fig. 2 and 3). The watershed covers approximately 9100 ha and encompasses a steep elevation and, hence, environmental gradient that spans hot, dry, semiarid desert scrub ecosystems at elevations near 800 m asl to cool, sub-humid, mixed conifer forests at high elevations, with a maximum elevation of ?2800 m asl. The underlying bedrock is dominated by Tertiary-aged granitic rocks at mid to upper elevations and Tertiary-aged mylonite, a metamorphosed granitic gneiss, at low to mid elevations, with sparse cover of Paleozoic metasedimen-tary rocks at the highest elevations (Dickinson, 1992). Soils exhibit minimal soil development across the gradient, with the greatest differences being a trend from shallow (<50 cm to saprock) to

moderately deep (100–150 cm to saprock) soils and increas-ing organic matter content with elevation (Lybrand et al., 2011; Pelletier et al., 2013; Whittaker et al., 1968).

Mean annual temperature decreases from near 22°C at low eleva-tions to a minimum near 6 to 7°C at high elevation. Mean annual precipitation follows an inverse pattern, with the lowest precipita-tion amounts of 250 mm yr−1 at low elevation and an increase to near 800 mm yr−1 at high elevation (Fig. 3a and 3b). All elevations possess a bimodal precipitation regime, with an approximate 50:50 split between winter and summer precipitation. The high-elevation systems above ?2000 m receive much of the winter precipitation as snow; however, these systems are sufficiently warm during the winter that they do not typically maintain a deep seasonal snow-pack, with winter climate patterns typified by pulses of snowfall and subsequent melt events (Heidbuchel et al., 2013).

Disturbance in the Sabino Creek watershed largely derives from wild-fire events, with wildfire recognized as a major driver of CZ processes and development in the western United States (Dennison et al., 2014; Holden et al., 2012; Littell et al., 2009; Westerling et al., 2003). The Sabino Creek watershed has been subjected to a number of fires during the last several decades, the most significant of which was the Aspen fire in 2003 that burned >7880 ha in the watershed or roughly 87% of the catchment area (Magirl et al., 2007). Burn severity maps

Fig. 2. Location of the Sabino Creek watershed in the Santa Catalina Mountains in southern Arizona. The watershed covers >9100 ha and spans an elevation gradient ranging from 580 m to 2800 m asl.

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derived from pre- and post-burn LandSat imagery (http://www.fs.usda.gov/detail/r3/landmanagement/gis/?cid=stelprdb5208076) indicated only ?760 ha of severe burn, or 8% of the catchment, with 3150 ha, or 35% of catchment area, of low severity to no burn (Fig. 3f). The levels of burn severity documented for the Aspen fire were used as a metric for characterizing disturbance effects on EEMT.

A high-resolution (1 m pixel−1 resolution) LiDAR data set (Pima Association of Governments, http://www.pagnet.org) for the SCM was used as the base set of elevation data for climate and topo-graphic modeling. Data products extracted from the LiDAR data included both the bare earth digital elevation model (DEM) and canopy height. The LiDAR data were rescaled to a 10 m pixel−1 resolution to facilitate rapid computational processing across the relatively large study area.

The three methods for calculating EEMT included: (i) EEMTTRAD based on simple energy and water balances and net primary produc-tion estimates; (ii) EEMTTOPO that captures topographic controls on energy, water, and C balances; and (iii) EEMTTOPO-VEG that integrates both topographic controls on water and energy balances and vegetation controls on surface resistance and primary produc-tion. All of these calculations rely on a base set of climate, solar radiation, and leaf area index data. Evapotranspiration and net pri-mary production for each method vary with: (i) EEMTTRAD relying on simple empirical approximations based on climate parameters; (ii) EEMTTOPO using a Penman–Monteith approach to estimate potential evapotranspiration coupled with a Budyko curve to approx-imate actual evapotranspiration and empirical estimates of primary production based on topography; and (iii) EEMTTOPO-VEG imple-menting a full Penman–Monteith approach to calculating actual evapotranspiration that includes pixel-based measures of surface and aerodynamic resistance and a canopy-height-based approximation of primary production. The parameters used for each approach are outlined below.

Local Climate, Solar Radiation, and Leaf Area DataLocal climate data were derived for a set of remote area weather sta-tions managed by the US Forest Service (http://www.raws.dri.edu/). Data from three stations in the Santa Catalina Mountains and adja-cent Rincon Mountains that span the full elevation gradient were processed for mean monthly minimum and maximum temperatures, precipitation, relative humidity, and wind speed. The three stations, Saguaro at 800 m asl, Soller Spring at 2300 m asl, and Rincon at 2512 m asl, have an average period of record of 12 yr, providing a reasonable climatological data set. Climate parameters including temperature, precipitation, relative humidity, and wind speed were regressed relative to elevation on a monthly basis, with most param-eters exhibiting a linear relationship to elevation (Supplemental Fig. S1). These relationships were used to calculate mean monthly clima-tological norms for each 10-m pixel in the study area and served as the base climate data for the modeling detailed below.

Solar RadiationTotal incoming shortwave solar radiation (direct and diffuse) was calculated on a monthly basis using the 10-m DEM and the solar radiation routine in ArcGIS 10.0 that accounts for variations in lati-tude, elevation, and aspect. The applied algorithm does not account for topographic shielding and shadowing and thus may overestimate radiation in certain portions of the landscape, particularly those associated with south-facing convergent areas that may experience morning shading from adjacent north-facing slopes (Beaudette and O’Geen, 2009). Incoming radiation was calculated incorporating topographic variation in slope and aspect, Stopo, as well as for a free flat surface with constant values of zero for slope and aspect, Sflat. The ratio of the two, Si = Stopo/Sflat, was used for modeling topo-graphic modifications of temperature (see below). Calculations for both Stopo and Sflat were performed on a monthly basis using a 2-h time step, a sky view of 200 pixels, 32 calculation directions, eight zenith and azimuth divisions, and uniform clear sky conditions.

Leaf Area IndexA leaf area index (LAI) was derived using a vegetation index approach that predicts LAI using a remotely sensed normalized difference vegetation index (NDVI). The 1 m pixel−1 resolution National Agriculture Imagery Program (NAIP) four-band imag-ery data collected for all of Arizona in June of 2010 that included red, blue, green, and near-infrared (NIR) spectra was used as the base data for calculating NDVI and LAI. The NDVI was calcu-lated from the NAIP NIR and red bands as (Huete et al., 1994) (NIR − Red)/(NIR + Red). The third-order polynomial function of Qi et al. (2000), derived for semiarid regions in southern Arizona, was used to calculate the LAI from the NDVI as ax3 + bx2 + c + d, where x is the NDVI and a, b, c, and d are 18.99, −15.24, 6.124, and

−0.352, respectively. Calculated values for LAI ranged from 0 to 9.5 for the study area. The LAI data were calculated at a 1 m pixel−1 reso-lution, then resampled to the 10 m pixel−1 resolution of the DEM.

Modeled values for LAI increased from a minimum of 0.1 in low-elevation desert ecosystems to 9.5 in the high-elevation mixed conifer ecosystems (Fig. 3e). The highest values for each elevation occurred on north-facing slopes and in drainageways where topography controls the local energy and water balance and water available for primary production. The largest impacts of recent wildfire activity on the LAI were noted in the high-elevation conifer ecosystems that experienced a high-severity, stand-replacing burn.

Topographically Modified TemperatureFollowing Moore et al. (1993), minimum, maximum, and mean monthly air temperatures (°C) at each pixel (Ti) were calculated using the local lapse rate, topographically modified solar radiation (Si), and LAI:

bb lapse

max

LAI11

1000 LAIi i

i ii

z zT T T C S

S

æ öæ öæ ö- ÷ ÷ç ç÷ç ÷ ÷= - + - -ç ç÷ç ÷ ÷÷ ç çç ÷ ÷ç çè ø è øè ø [6]

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where Tb is the temperature (°C) at a base station; Tlapse is the local lapse rate (°C km−1); zi and zb are the elevation (m) of the pixel and base station, respectively; C is a constant equal to 1; Si is the ratio between direct shortwave radiation on the actual surface and direct shortwave radiation on a horizontal surface; LAIi is the pixel leaf area index; and LAImax is the maximum value for LAI, equal to 10.

The mean monthly minimum and maximum temperatures (Tmin and Tmax) were calculated using the monthly minimum and maxi-mum temperature lapse rates derived from the climate station and elevation data. The low-elevation station was selected as the base station for determining both Tb and zb. The minimum tempera-ture was calculated using only the minimum temperature lapse rate, i.e., ignoring the second term in Eq. [6], because minimum temperatures occur at night when there is a negligible effect of solar radiation or LAI on the temperature. The mean monthly tempera-ture was calculated as the average of Tmin and Tmax.

The amount of information included in the temperature calcula-tions varied with each EEMT modeling approach. Specifically, EEMTTRAD used temperature calculated using only the derived lapse rates; EEMTTOPO incorporated the solar radiation term but did not include LAI; and EEMTTOPO-VEG included all terms in Eq. [6].

Local Water BalanceThe wetting of each pixel per month was approximated using a local water balance (L’vovich, 1979):

PPT SR AETW F= - = + [7]

where W is pixel wetting (m s−1), PPT is the mean annual precipita-tion, SR is surface runoff, AET is actual evapotranspiration, and F is the water partitioned to base flow. The F term quantifies sub-surface wetting, a key parameter for calculating EEMT (see below), and represents the fraction of water with the ability to transfer heat energy and perform chemical and physical work in the subsur-face. Equation [7] may be rewritten to solve for F as F = Peff − SR, where Peff is the effective precipitation, equivalent to PPT − AET. Effective precipitation is thus a key component of the water bal-ance approach applied here and central to calculating EEMT. The three approaches to modeling EEMT varied in the calculation of Peff and specifically the calculation of the AET term, as described below. The length scale of precipitation and evapotranspiration were scaled to units of mass per unit area per unit time based on the density of water and the assumption that a meter of precipitation is equivalent to 1 m3 H2O m−2.

Evapotranspiration for Traditional Effective Energy and Mass TransferWe applied three techniques for calculating the actual evapo-transpiration that incorporate various levels of detail of

environmental data. The original formulation of EEMT (Rasmussen et al., 2005) relied on a very simple water bal-ance approach commonly used in pedologic studies wherein Peff was determined as the difference between monthly pre-cipitation and potential evapotranspiration (PET) calculated using the Thornthwaite and Mather (1957) temperature-based approach. In the calculation of EEMTTRAD in this study, we calculated PET using Hamon’s equation (PETH) that incorpo-rates temperature, daylight, and saturated vapor pressure (see Supplemental Material) and provided values nearly identical to the Thornthwaite–Mather approach across the study area (Haith and Shoemaker, 1987; Hamon, 1961).

Evapotranspiration for Topographically Modified Effective Energy and Mass TransferThe modeling approach for EEMTTOPO was designed to explicitly incorporate topographic variations in solar radiation, tempera-ture, wind speed, and vapor pressure deficit. Specifically, PET was calculated using a Penman–Montieth approach to estimate pan evaporation (see Supplemental Material) that was then coupled with an estimation of the AET using a Budyko curve (Budyko, 1974) describing the partitioning of potential and actual evapo-transpiration relative to the aridity index (ratio of annual PET to annual rainfall). Potential evapotranspiration and precipitation were converted to monthly values of AET (m s−1) using a Zhang–Budyko curve that describes the climatological relationship between the relative partitioning of catchment-scale precipitation to PET and AET as (Zhang et al., 2001)

pm pmZB

1/PET PET

AET PPT 1 1PPT PPT

wwì üï ïé ùï ïæ öï ïê ú÷ï ïç ÷= + - +çí ýê ú÷ç ÷ï ïçè øê úï ïë ûï ïï ïî þ

[8]

where w is an empirical constant, here set equal to 2.63 following Zhang et al. (2004). This catchment-scale approach to precipitation partitioning was then scaled to local topography based on incor-poration of topographic redistribution of effective precipitation (below). It is likely that w varies with the local climate, vegetation, and subsurface storage regimes that span the study watershed, e.g., Zhang et al. (2004) determined optimum w values ranging from 2.15 to 3.75 for temperate forest and grassland systems, respectively. However, for simplicity and the lack of a clear empirical means to assign a w value to specific ecosystems, we applied a constant value of w to all ecosystems.

Evapotranspiration for Topographic and Vegetation Modified Effective Energy and Mass TransferThe approach to calculating EEMTTOPO-VEG used the Penman–Montieth equation that includes the surface resistance term in the denominator and a canopy-derived estimate of aerodynamic resistance to provide an estimate of the actual evapotranspiration (AETpm) (see Supplemental Material). The aerodynamic resistance

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term was calculated using the canopy height derived from the LiDAR data, and surface resistance was estimated from the LAI. Following data reported by Schulze et al. (1994) and Kelliher et al. (1995), we fit a polynomial function relating bulk surface conductance to LAI assuming a maximum leaf stomatal conductance of 0.008 m s−1. This approach does not account for species- and ecosystem-level dif-ferences in stomatal conductance. The ecosystems included in the study area range from desert scrub to mixed conifer forests. Previous research has indicated that the maximum stomatal conductance mea-sured in various conifer species to sclerophyllous shrubs ranges from 0.0038 to 0.0082 m s−1, comparable to the 0.008 m s−1 value used here (Kelliher et al., 1995). Surface resistance was taken as the inverse of the bulk surface conductance, with values ranging from 38 to 55 s m−1. For any months of AETpm > PPT, we assumed that AET was equivalent to PPT and Peff was set equal to zero.

Topographic Water RedistributionThe wetting of each pixel is a function of both effective precipita-tion and surface runoff as noted in the rearrangement of Eq. [7] to F = Peff − SR. It is thus necessary to account for topographic redistribution and partitioning of precipitation to quick surface runoff in addition to local-scale variation in Peff. One standard approach to empirically quantifying topographic control on water redistribution is the topographic wetness index, calculated as (Beven and Kirkby, 1979) l = ln(a/tanb), where a is the unit or specific catchment area in meters, calculated here using the D-inf multiple-flow-direction algorithm for flow routing (Tarboton et al., 1991), and b is the slope in degrees. The wetness index pro-vides empirical measures of relative landscape wetness but does not provide a mass-conservative approach to redistributing effective precipitation across a catchment.

We developed a modified topographic wetness index, referred to as the mass conservative wetness index (MCWI) and denoted with the symbol a , which accounts for topographic redistribution of effective precipitation and maintains conservation of mass of catchment-scale precipitation inputs. We argue that ai is propor-tional to the local pixel wetness index (li) normalized to the mean catchment wetness index (l ):

ii

la µ

l [9]

such that ai = li/(1/N)Sli and Sai = N, where N is the number of pixels in a catchment. The normalization ensures conservation of mass of the effective precipitation term for a given catchment. The scalability of ai was tested by comparing estimations of ai using l calculated for both local subcatchments and for the entire study area (Supplemental Fig. S2); the 1:1 scaling between the two values indicates that there is not a catchment-size effect on ai.

Calculated MCWI values ranged from 0.4 to 3.4, with the lowest values on divergent hillslope summits and ridgelines and the greatest values in drainageways, particularly the low-elevation

drainageways that have large catchment areas (Fig. 3c). These values indicate that local effective precipitation may be reduced by up to 60% due to runoff, whereas drainageways may receive water (as soil moisture) in excess of up to 340% over local effective precipitation inputs.

The fraction of monthly Peff partitioned to F at each pixel (Fi, m s−1) using this modified topographic wetness index was deter-mined as

effi i iF P=a [10]

Primary Production and Standing BiomassNet primary production was calculated differently for each EEMT modeling approach, reflecting incorporation of increas-ing levels of topographic and vegetative information. The NPP calculation for EEMTTRAD was based on the temperature of the months in which precipitation is greater than evapotranspiration. For these months, NPP was calculated following Lieth (1975): NPP = 3000[1 − exp(1.315 − 0.119T)]−1. Using this equation, NPP was calculated on a monthly time step for all months of PPT > PET, and NPP was scaled to a monthly time step based on each month’s percentage of 1 yr. This method of NPP estima-tion does not account for primary production that occurs using stored soil moisture and thus probably underestimates total NPP. However, comparison of NPP calculated using this method relative to global NPP data sets indicates reasonable agreement between the two (Rasmussen and Gallo, 2013; Rasmussen et al., 2005).

For the EEMTTOPO approach, we incorporated information on elevation and aspect using an empirical function fit to NPP data presented by Whittaker and Niering (1975) for the SCM. Aspect and slope were converted to the unitless parameter “northness,” which is the product of the cosine of aspect and the sine of slope and ranges from −1 for a south-facing, vertical cliff to 1 for a north-facing vertical cliff (Fig. 3d). Total annual aboveground NPP (g m−2 yr−1) was regressed against elevation and northness with the best-fit multiple linear regression model of

NPP 0.39 346 187z n= + - [11]

where z is elevation in meters and n is northness, with r2 = 0.82, P < 0.0001, and RMSE = 168 g m−2 yr−1. Any predicted values <100 g m−2 yr−1 were adjusted to 100 g m−2 yr−1 to match the minimum NPP measurements in the Whittaker and Niering (1975) data set.

For the EEMTTOPO-VEG approach, annual NPP (g m−2 yr−1) was calculated as a function of canopy height, derived from the LiDAR data, using a polynomial function relating canopy height and aboveground NPP using data reported by Whittaker and Niering (1975):

Vadose Zone Journal p. 9 of 16

( )2NPP 196 36 0.61 12.0933h h= + - - [12]

where h is canopy height (m) derived from the LiDAR data, with r2 = 0.89, P < 0.0001, and RMSE = 130 g m−2 yr−1.

Standing biomass (Mg ha−1) was calculated from the LiDAR mean canopy height (mch) profile (Asner et al., 2011; Lefsky et al., 1999; Mascaro et al., 2011). The model parameters were determined from a regression of the field-measured biomass from 13 0.1-ha plots in the SCM (1.3 ha), 79 0.05-ha plots in the Pinaleño Mountains, Arizona (3.65 ha), and 48 0.1-ha plots in the Jemez River Basin, New Mexico (4.8 ha) (Swetnam, 2013):

2.151Biomass 1.441 mch= [13]

All three study areas shared the same plant functional type groups (Smith et al., 1997), where the presence and frequency of species in the stand are all closely related. Average biomass measured in the SCM plots was 226.66 ± 125.84 Mg ha−1; the peak quantity of biomass measured in any plot in the three study areas was in the Pinaleño Mountains, where an equivalent of 1495 Mg ha−1 was measured in the 0.05-ha plots. Similar stand conditions and life histories are shared between the Pinaleño Mountains and the SCM (Niering and Lowe, 1984; Whittaker and Niering, 1975). In a similar plot in the SCM (white fir [Abies concolor (Gordon & Glend.) Lindl. ex Hildebr.] ravine forest), Whittaker and Niering reported 790 Mg ha−1 of aboveground biomass.

Effective Energy and Mass TransferThe individual components of EEMT were calculated as in Eq. [4] and [5] and the EEMT term calculated as in Eq. [3] for each pixel on a monthly basis. To summarize, the three approaches to calculating EEMT varied in the derivation of the F and NPP terms and incorporated greater levels of environmental informa-tion. Specifically: (i) EEMTTRAD was based on F derived from the balance of precipitation and PET and NPP derived using the Lieth empirical function; (ii) EEMTTOPO was calculated based on F derived using the coupled Penman–Budyko approach to cal-culating AET and the MCWI to account for local variations in water redistribution, and NPP was calculated from the empirical

relationship between NPP, northness, and elevation; and (iii) EEMTTOPO-VEG was calculated using F derived from the bal-ance of precipitation and AET calculated using Penman–Monteith that accounted for local surface resistance and canopy-influenced aerodynamic resistance, the MCWI to account for local variations in water redistribution, and NPP derived from the empirical rela-tionship between LiDAR-measured canopy height and NPP. The correlation among environmental variables and the various EEMT values are presented in Supplemental Table S1, with an analysis of factor importance to EEMT prediction for each method determined using a simple multiple linear regression approach (Supplemental Table S2).

6Results and DiscussionWatershed Climate ClassificationClimate forcing parameters of temperature and precipitation vary consistently and inversely with elevation across the study area, i.e., decreasing temperature and increasing precipitation with increas-ing elevation, as is typical of mountainous ecosystems in the Desert Southwest (DeBano et al., 1995) (Fig. 3a and 3b). Climate across the watershed was characterized using an aridity index derived from modeled climate parameters to account for this covariance and to facilitate a simpler discussion of EEMT variation with climate and elevation. Values for the aridity index, defined as the ratio between PETH and MAP, ranged from a maximum of 2.5 in the low-ele-vation systems to a minimum of 0.6 in the high-elevation systems. The PETH/MAP data were classified into five classes using a hier-archical classification scheme based on Ward’s minimum variance method to define the distance between classes (Milligan, 1979). The number of classes was determined by iterating with various num-bers of classes, ranging from 3 to 10. It was determined that five was the fewest number of classes required to best capture the transition in climate from water-limited (PETH/MAP > 1) to energy-limited (PETH/MAP < 1) systems. The classification scheme was specifi-cally focused to capture the transition from energy- to water-limited systems because this represents a key transition in hydrologic func-tion and vegetation composition (Brooks et al., 2011). The five classes were categorized and named based on PETH/MAP ranges into the following (Table 1):

Table 1. Aridity class potential evapotranspiration/mean annual precipitation (PET/MAP) values and associated elevation, vegetation, and effective energy and mass transfer using the traditional method (EEMTTRAD), EEMT with topographic controls (EEMTTOPO), and EEMT with both topo-graphic and vegetation controls (EEMTTOPO-VEG).

Aridity index class PET/MAP Elevation Canopy height Biomass EEMTTRAD EEMTTOPO EEMTTOPO-VEG

m m Mg ha−1 ——————————— MJ m−2 yr−1 ———————————

Humid 0.70 ± 0.05† 2433 ± 113 5.44 ± 4.57 104.9 ± 190.7 33.7 ± 2.9 23.1 ± 3.4 21.2 ± 11

Humid transition 0.89 ± 0.07 2080 ± 115 2.34 ± 2.19 19.4 ± 56.4 24.4 ± 3.2 19.1 ± 3.5 12.1 ± 5.8

Arid transition 1.18 ± 0.09 1683 ± 101 1.19 ± 1.18 4.9 ± 17.3 14.1 ± 2.4 15.0 ± 3.8 9.0 ± 3.1

Semiarid 1.51 ± 0.1 1365 ± 84 0.78 ± 1.03 2.9 ± 20.6 7.6 ± 1.0 11.4 ± 3.4 7.6 ± 2.1

Arid 1.97 ± 0.2 1063 ± 107 0.77 ± 0.76 1.9 ± 9.9 5.5 ± 0.5 8.0 ± 3.1 6.7 ± 1.4

† Mean ± 1s.

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1. Humid with a range of 0.6 to 0.8

2. Humid transition with a range of 0.8 to 1.0

3. Arid transition with a range of 1.0 to 1.3

4. Semiarid with a range of 1.3 to 1.7

5. Arid with a range of 1.7 to 2.5

The classes correspond with an approximate 300-m elevation gain interval and with changes in vegeta-tion community (Table 1), grading from humid classes at high elevation dominated by coniferous ecosystems, to transitional classes at mid-eleva-tion that include the transition from open grass oak woodland to mixed oak and pine forest plant communities, to arid classes at low elevation occu-pied by desert scrub. Canopy height and biomass increased with elevation and wetness (Table 1). Vegetation assemblage and LAI followed the varia-tion in elevation-controlled climate parameters and local topographic controls on MCWI and north-ness (Fig. 3).

Measures of Effective Energy and Mass TransferTraditional Effective Energy and Mass TransferValues for EEMTTRAD ranged from a low near 5 MJ m−2 yr−1 in low-elevation, very dry desert scrub systems to a maximum of just over 42 MJ m−2 yr-1 in the wet, mixed conifer, high-elevation systems (Fig. 4a). The values varied directly with elevation following the elevation control on climatological parameters. This range of values corresponds well with EEMTTRAD ranges calculated previously using the 4-km and 800-m pixel resolution PRISM climate data set (Rasmussen et al., 2005) that ranged from 10 to 35 MJ m−2 yr−1, and with an initial attempt to incorporate topography into EEMT esti-mates at a 10-m pixel resolution using an empirical relationship derived among EEMT, temperature, precipitation, and vapor pressure deficit (Chorover et al., 2011) that ranged from <5 to 37 MJ m−2 yr−1.

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class (Table 2). Values for EEMTTOPO were generally on the order of 5 MJ m−2 yr−1 greater on north-facing slopes than south-facing slopes, with the largest difference of 5.7 MJ m−2 yr−1 noted in the arid transition class and the smallest difference of 4.6 MJ m−2 yr−1 observed in the arid class. Similarly, EEMTTOPO values tended to be greater in water-gaining portions of the landscape, with values on average 1.4 MJ m−2 yr−1 greater in areas with MCWI values >1. The largest EEMTTOPO difference of 1.9 MJ m−2 yr−1 was observed in the humid transition class, with the smallest differ-ence 0.6 MJ m−2 yr−1 observed in the arid class.

Aspect and topographic wetness had varying impacts on EEMTTOPO, with some variation among aridity classes (Table 2). Generally greater values of EEMTTOPO were predicted on north-facing slopes, with values averaging 5 MJ m−2 yr−1 greater on slopes with northness values >0 (Table 2). The smallest aspect difference of 4.6 MJ m−2 yr−1 was observed in the arid class, where differ-ences were probably minimized due to the overall aridity of this portion of the SCM. In comparison, the largest aspect difference of 5.7 MJ m−2 yr−1 was observed in the arid transition class on the boundary of water and energy limitation, where aspect-controlled variation in radiative forcing and temperature produced greater dif-ferences in water availability and primary production. The values for EEMTTOPO for north-facing slopes in a given aridity class generally corresponded closely to the mean EEMTTOPO values for south-facing slopes in the next wetter class, e.g., an average EEMTTOPO value of 22.5 MJ m−2 yr−1 on the north-facing slopes in the humid

transition class relative to an average of 21.2 MJ m−2 yr−1 on the south-facing slopes in the humid class. This pattern was consistent across all aridity classes, indicating that north-facing slopes in a given climate zone function similarly to wetter ecosystems, equiva-lent to an approximate 300-m elevation gain (Table 1). A similar pattern has been observed in vegetation patterning and soil proper-ties across the SCM (Lybrand and Rasmussen, 2014; Pelletier et al., 2013; Whittaker et al., 1968) and other elevation gradients in the western United States (Poulos et al., 2010).

Variation in EEMTTOPO between water-gaining (MCWI > 1) and water-losing (MCWI < 1) landscape positions were less pronounced than those associated with aspect, with an average increase of 1.4 MJ m−2 yr−1 in water-gaining portions of the landscape. The difference between losing and gaining positions increased with moisture availability and aridity index class (Table 2), probably a function of greater water available to redistribute to gaining portions of the landscape. The MCWI as applied here does not account for runoff response to rainfall characteristics, e.g., high-intensity monsoon rainfall that may exceed surface soil infiltration rates with the potential for substantial water redistribu-tion from losing to gaining portions of the landscape even in the semiarid and arid systems (Zhang et al., 2011).

Effective Energy and Mass Transfer with Topographic and Vegetation Control The va lues for EEMT TOPO-V EG ranged from 2 .5 to

63.4 MJ m−2 yr−1, increasing from low to high elevation similar to the other values for EEMT (Fig. 4c). The highest values of EEMT, 35 to 63 MJ m−2 yr−1, were spatially constrained to those areas with an elevation greater than ?2000 m asl and PETH/MAP < 1.0, cor-responding to predominantly pine and mixed conifer ecosys-tems. Differences in EEMT with aspect and topographic wetness averaged 3.9 and 0.9 MJ m−2 yr−1, respectively, but exhibited substantial variation with aridity index class (Table 3). The EEMT differences by aspect increased with increasing water availability, with a large increase in the relative differences observed in the humid class. Similar to values predicted for EEMTTOPO, average north-aspect EEMTTOPO-VEG values for a given aridity class were compa-rable to average EEMTTOPO-VEG values for south-facing slopes in

Table 2. Mean effective energy and mass transfer with topographic controls (EEMTTOPO) by aspect and wet-ness index grouped by aridity index class.

Aridity index class

Aspect Wetness index

North South Difference Gaining Losing Difference

Humid 26.2 ± 2.71† 21.16 ± 2.19 5.04 ± 0.01 24.03 ± 3.35 22.49 ± 3.34 1.54 ± 0.014

Humid transition 22.45 ± 2.57 17.43 ± 2.56 5.02 ± 0.01 22.45 ± 2.57 17.43 ± 2.56 1.91 ± 0.013

Arid transition 18.65 ± 2.87 12.98 ± 2.45 5.67 ± 0.013 20.39 ± 3.5 18.48 ± 3.29 1.55 ± 0.019

Semiarid 14.37 ± 2.25 9.24 ± 2.3 5.13 ± 0.011 18.65 ± 2.87 12.98 ± 2.45 1.3 ± 0.017

Arid 10.72 ± 2.35 6.11 ± 1.81 4.61 ± 0.012 16.04 ± 3.67 14.49 ± 3.71 0.64 ± 0.018

Mean 5.08 ± 0.34 1.39 ± 0.42

† Mean ± 1s.

Table 3. Mean effective energy and mass transfer with topographic and vegetation controls (EEMTTOPO-VEG) by aspect and wetness index grouped by aridity index class.

Aridity index class

Aspect Wetness index

North South Difference Gaining Losing Difference

Humid 26.69 ± 11.11† 18.07 ± 9.14 8.62 ± 0.04 22.89 ± 11.55 20.39 ± 10.13 2.49 ± 0.043

Humid transition 15.01 ± 6.41 10.78 ± 4.84 4.22 ± 0.021 12.99 ± 6.47 11.78 ± 5.34 1.22 ± 0.022

Arid transition 10.94 ± 2.19 7.92 ± 2.48 3.02 ± 0.014 9.11 ± 2.98 8.96 ± 3.19 0.15 ± 0.016

Semiarid 8.81 ± 1.56 6.67 ± 1.92 2.13 ± 0.009 7.78 ± 1.92 7.49 ± 2.13 0.28 ± 0.01

Arid 7.43 ± 1.05 6.09 ± 1.34 1.34 ± 0.007 6.89 ± 1.36 6.51 ± 1.39 0.38 ± 0.008

Mean 3.87 ± 2.56 0.90 ± 0.88

† Mean ± 1s.

Vadose Zone Journal p. 12 of 16

the next wetter humidity class. Differences in EEMTTOPO-VEG between water-gaining and water-losing landscapes increased with increasing water availability, but overall exhibited minimal varia-tion. In general, the largest impacts of topography and vegetation on EEMTTOPO-VEG values were observed in the energy-limited humid ecosystems that are dominated by mixed conifer vegetation assemblages and are the most biologically productive (Whittaker and Niering, 1975). These systems also exhibit the greatest soil C stocks, degree of chemical weathering, and soil development (Lybrand and Rasmussen, 2014).

Vegetation Effects on Effective Energy and Mass TransferThe effects of vegetation on the calculated EEMT was evident in the spatial patterning exhibited in EEMTTOPO-VEG (Fig. 4c). This result was expected because vegetation is incorporated into energy, water, and C balances through the LAI constraint on surface tem-perature estimates (Eq. [6]), the surface resistance term in AET estimates, and the modeled relation of canopy height to NPP (Eq. [12]). Multiple linear regression analysis of EEMTTOPO-VEG rela-tive to elevation, northness, MWCI, and canopy height indicated that canopy height was the most important factor accounting for variations in EEMTTOPO-VEG (Supplemental Table S2). In par-ticular, predictions of AET using Penman–Monteith are highly sensitive to surface resistance (Shuttleworth, 1993). The predicted surface resistance estimates were reasonable and in the range of 38 to 55 s m−1 but probably introduce the largest source of error and spatial variation into the water balance used to calculate EEMTTOPO-VEG.

We further examined the relative impact of vegetation incorpo-ration into EEMT estimates through comparison of the ratio between EEMTTOPO-VEG and EEMTTOPO by aridity class (Fig. 5a). The data were a subset of data for those locations with no or low burn severity to avoid any confounding effects of fire. Values for EEMTTOPO-VEG/EEMTTOPO indicated minimal differences in EEMT estimates for the arid and humid classes, with mean ratios of 1.08 and 0.91, respectively. The largest differences between the two methods for calculating EEMT were observed for the humid transition and arid transition classes, with average ratio values of 0.62, indicating that EEMTTOPO values were greater than EEMTTOPO-VEG values. The differences between the two EEMT values are a direct function of vegetation in that EEMTTOPO-VEG incorporates the current vegetation structure into its estimates of water and C fluxes. We suggest that EEMTTOPO provides a maxi-mum “potential” estimate of EEMT, whereas EEMTTOPO-VEG reflects current or “actual” energy and mass transfers based on the current vegetation structure.

The greatest difference between the two estimates was observed at the water- to energy-limited transition zone. This zone probably represents the zone of greatest dynamism in vegetation structure and composition because it bounds the transition zone in the water

balance and is associated with the transition from mainly grass, shrub, and open woodland plant communities to more mixed pine and oak forest (Whittaker and Niering, 1975). The current vegeta-tion structure in this zone is probably a function of both longer term, e.g., centennial time scales, and shorter term, e.g., annual to decadal, fluctuations in climate-controlled water availability and drought. Climate fluctuation is also coupled with the time scales of the vegetation response to changes in climate that vary with vegetation type, e.g., long-lived trees may not reflect recent changes in water availability that would favor more temporally dynamic grasses and shrubs (Walther et al., 2002).

The spatial patterns of EEMTTOPO-VEG, particularly at high elevations (Fig. 4c), indicated a negative trend to increasing burn severity class from the 2003 Aspen fire that occurred approxi-mately 7 yr before acquisition of the NAIP image and LiDAR collection. The differences in EEMTTOPO-VEG and EEMTTOPO

Fig. 5. Comparison of the natural logarithm of the ratio between effective energy and mass transfer with topographic controls (EEMT-TOPO) and effective energy and mass transfer with topographic and vegetation controls (EEMTTOPO-VEG) by (a) aridity/humidity class and (b) burn severity. Ratio values of 1 indicate identical values for the two measures of EEMT, denoted by a dashed line in both figures. Deviation from the 1 line indicates divergence between the two mea-sures of EEMT.

Vadose Zone Journal p. 13 of 16

increased significantly with increasing burn sever-ity, with ratio values decreasing from a mean of 0.95 for areas that did not burn, to a mean of 0.64 for the high-severity burn areas (Fig. 5b). Lower ratios suggest a greater differential between maxi-mum potential EEMT and actual EEMT recorded in the current vegetation structure. Disturbance events, such as wildfire, that remove vegetation and alter local patterns of evaporation and primary production thus serve to reduce the modeled values of EEMTTOPO-VEG relative to the idealized condi-tions modeled with EEMTTOPO.

Biomass Relationship to Effective Energy and Mass TransferThe average 10-m pixel mean canopy height across the Sabino Creek watershed ranged from 0 to 26 m, with the biomass estimated to range from 19 to 1600 Mg ha−1 based on the 99.5% quantile of canopy height and biomass values. The 99.5% quantiles were used to exclude very high values of canopy height that yield unreasonably high biomass values. The 99.5% quantile values were similar to independent measures of aboveground biomass in the SCM (Whittaker and Niering, 1975) and Pinaleño Mountains nearby in southeastern Arizona (Pelletier et al., 2013; Swetnam, 2013) that reported maximum measurements on the order of 790 to 1500 Mg ha−1, respectively.

Both EEMTTOPO and biomass exhibited simi-lar patterns of increase with both elevation and northness (Fig. 6), suggesting that EEMTTOPO may be used to predict the maximum biomass for a given area. Direct comparison of biomass to EEMTTOPO indicated a power law relationship in the form of Biomass = mEEMTTOPO

b. The power function was fit to the 99.5% quantile of biomass and EEMTTOPO, yielding parameters of m = 0.032 ± 0.0075 kg m2 yr ha−1 MJ−1 and b = 3.22 ± 0.071, with an equation fit of r2 = 0.98, P < 0.0001, and RMSE of 69.7 Mg ha−1 (Fig. 7). The model fit well the overall trend in the data, with the largest discrepancy between actual and predicted values noted near the inflection point of the function at EEMTTOPO values of ?12 to 18 MJ m−2 yr−1. This zone corresponds with the dry and wet transition humidity classes and suggests a possible break in scaling between biomass and EEMTTOPO. At high values of EEMTTOPO, biomass tended to decrease. These areas correspond to those impacted by moderate and severe burns and a loss of standing biomass. The power law relationship suggests that EEMTTOPO may provide an upper bound estimate for standing biomass for what the potential for aboveground biomass could attain in these areas. The relation-ship of biomass to EEMTTOPO probably reaches a plateau beyond EEMTTOPO values of 35 to 40 MJ m−2 yr−1, as suggested by global

upper limits on aboveground biomass in temperate conifer forests on the order of 1600 to 1800 Mg ha−1 (Keith et al., 2009).

Comparison of Effective Energy and Mass Transfer Values to Soil DepthThe separate sets of EEMT values were directly compared with measured and modeled values of soil depth for a small ?5-ha for-ested catchment in the headwaters of Sabino Creek as a means to document the relative improvement that incorporation of topog-raphy and vegetation into EEMT imparts on predicting pedon- to hillslope-scale CZ structural variation. The soil depth data derive from previous work in the SCM and represent the most robust set of soil depth data we have collected to date (Holleran et al., 2014; Pelletier and Rasmussen, 2009). The catchment is at a mean eleva-tion of 2400 m asl, with mixed conifer vegetation, granitic parent material, and soils that include a combination of Entisols on ridges and slopes and Mollisols in convergent water-gathering portions of the landscape (Holleran, 2013; Lybrand and Rasmussen, 2014). The soil depth data included 24 pedons and soil depth derived from a numerical model describing soil production and mass transport.

Fig. 6. Variation in (a) effective energy and mass transfer with topographic controls (EEMTTOPO) and (b) the upper 99.5% quantile of biomass by topographic northness (a combination of aspect and slope) and elevation. The data indicate that both values increase with elevation and northness in a similar pattern.

Vadose Zone Journal p. 14 of 16

Measured and modeled soil depths range from ?0.15 m on ridgetops to >2 m in convergent areas of the landscape. Values for EEMTTRAD, EEMTTOPO, and EEMTTOPO-VEG were extracted for each pedon location and modeled soil depth pixel. Simple cor-relation analyses revealed significant variation in the relationships among the sets of EEMT values and the soil depth data (Table 4). The vales for EEMTTOPO exhibited the strongest and most significant positive correlations to both measured and modeled soil depth data, indicating that incorporation of topographic con-trols on local energy and water balance and primary productivity significantly increased the positive relationship between EEMT and pedon- to hillslope-scale measures of CZ structural variability.

The relative lack of correlation between soil depth and EEMTTOPO-

VEG suggests that, for this location, the current vegetation stand has minimal influence on soil depth. The variance in EEMTTOPO-

VEG is largely attributed to canopy height data (Supplemental Table S2) that represent only one snapshot in time. We suggest that EEMTTOPO presents a stronger relationship than EEMTTOPO-

VEG because it better captures spatial patterns in the long-term average, i.e., >103 yr, fluxes of water and C into the subsurface,

whereas EEMTTOPO-VEG captures only the modern signature that may not reflect longer time scale patterns. This was clearly demonstrated in the large discrepancy between EEMTTOPO and EEMTTOPO-VEG for areas that recently experienced severe wildfire. Estimations of EEMTTOPO-VEG may be improved by incorporat-ing decadal scale time series of canopy height and LAI that better describe longer term patterns of vegetation structure and localized primary production. The data suggest that EEMTTOPO presents the more robust predictor of CZ structure, function, and evolu-tion over the long term and represents a measure of the potential or optimum influx of energy and mass to the CZ.

6SummaryThe analyses in this study indicated clear patterns in the EEMT to the subsurface CZ with topography and vegetation. Incorporating greater levels of environmental information introduced greater local complexity in EEMT, with clear variation in EEMT by aspect and with current vegetative cover. Key findings include:

• Greater values of EEMT were observed on north-facing slopes within a given aridity class and elevation zone, equiva-lent to a 300-m elevation gain. This pattern corresponds with observed aspect variation in modern canopy height and indicates clear aspect control on energy and mass influxes to the CZ that are probably important to understanding aspect-controlled variation in CZ evolution, structure, and function.

• The largest discrepancies in EEMTTOPO and EEMTTOPO-VEG were observed at the water- to energy-limited system transition where current vegetation structure is highly sensitive to local variations in the water and energy balances. Disturbance in the form of stand-replacing wildfire also substantially reduced estimates of EEMTTOPO-VEG relative to EEMTTOPO as a result of a reduction in biomass, primary productivity, and variations in surface and aerodynamic resistance. The discrepancy between the two EEMT values indicates deviation between what could be considered the long-term average energy and mass influx, or EEMTTOPO, and the current vegetation stand controlled energy and mass influx, or EEMTTOPO-VEG.

• A power law relationship was observed between aboveg-round biomass and EEMTTOPO, indicating the potential for using EEMTTOPO to predict an upper bound for biomass in a given area.

• The incorporation of topography and vegetation signifi-cantly increased the correlative relationship between EEMT and subsurface CZ structure as quantified here as soil depth. In particular, EEMTTOPO exhibited the strongest positive correlation to measured and modeled values of soil depth, in-dicating that this version of EEMT may serve as an effective predictor of CZ properties that captures pedon- to hillslope-scale variation in water and C influxes.

Fig. 7. Relationship between effective energy and mass transfer with topographic controls (EEMTTOPO) and biomass. Dark gray sym-bols are those points within the 99.5% quantile; light gray points are greater than the 99.5% quantile. The black line is the best-fit power law function in the form of: Biomass = mEEMTTOPO

b, where m is 0.032 and b is 3.22 with an RMSE of 69.7 Mg ha−1.

Table 4. Pairwise correlation of soil depth data and effective energy and mass transfer using the traditional method (EEMTTRAD), EEMT with topographic controls (EEMTTOPO), and EEMT with both topographic and vegetation controls (EEMTTOPO-VEG) for a small catchment in the headwaters of Sabino Creek. The data include point-measured (pit) soil depth data and numerically modeled soil depth data for the selected catchment.

EEMT method

Pit data (n = 24) Model data (n = 319)

r P value r P value

EEMTTRAD −0.038 0.861 −0.058 0.298

EEMTTOPO 0.385 0.063 0.569 <0.0001

EEMTTOPO-VEG −0.019 0.929 0.131 0.019

Vadose Zone Journal p. 15 of 16

AcknowledgmentsThis research was supported by the U.S. National Science Foundation Grants EAR-0724958630 and EAR-1331408 provided in support of the Catalina-Jemez Critical Zone Observatory.

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